The present invention relates generally to the design and fabrication of resonators. Resonators formed in accordance with the present invention find application, for example, within oscillators. Within the field of micro-electro-mechanical systems (MEMS), oscillators are critical components. The functionality of many micro-mechanical structures, including oscillators, is based on the reaction (e.g., oscillation, deflection, or torsion) of a spring mechanism to an applied force. Such “spring mechanisms” are typically formed from one or more beam structures having, or modeled to have, a rectangular cross section of predetermined width. The physical structure of a spring mechanism is typically formed using a sequence of planar or surface micro-machining fabrication processes. The degree to which a spring mechanism actually takes the form intended by its design is a function of the precision with which the one or more fabrication processes are applied to a layer or segment of a constituent material used to form the spring.
Fabrication processes are applied with well-understood tolerances. That is, variations normally occurring in the application of a particular fabrication process result in a micro-mechanical structure having physical dimensions that vary from its design specifications. For relatively large structures, such small, process-tolerance-induced variations are immaterial. However, MEMS components are so small and their functionality so demanding that even relatively minor variations from specification will adversely influence performance.
For example, the anisotropy of an etching method used to form a beam structure will determine the exact width of the beam and any variance of that width from design specifications. Line width control during lithography processes will similarly influence the physical dimensions of a beam structure.
Process-tolerance-induced variations can result in spring mechanisms having actual widths that differ greatly from their intended design. Since a spring mechanism's width defines its stiffness, and since the ratio of resonator stiffness to resonator mass defines a resonator's frequency response to an external stimulus, significant variations in spring width are unacceptable. Currently in the known quartz resonators, such variations are corrected by trimming the mechanical structure to better define its frequency in relation to its intended design. However, trimming for silicon based resonators is not a fabrication solution readily adapted to the reliable mass manufacture of resonator components. In order to produce precise resonators using silicon batch processing, a better design and/or fabrication solution is required.